TSTP Solution File: SWV911-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV911-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Wed Jul 20 21:45:35 EDT 2022

% Result   : Unsatisfiable 0.50s 0.69s
% Output   : Refutation 0.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   24 (  15 unt;   1 nHn;  24 RR)
%            Number of literals    :   35 (   0 equ;  18 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   24 (  24 usr;  14 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(203,axiom,
    equal(c_Collect(u,v),u),
    file('SWV911-1.p',unknown),
    [] ).

cnf(373,axiom,
    equal(c_Collect(c_COMBK(c_False,tc_bool,u),u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),
    file('SWV911-1.p',unknown),
    [] ).

cnf(461,axiom,
    equal(hAPP(hAPP(c_Set_Oinsert(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Collect(hAPP(c_fequal(u),v),u)),
    file('SWV911-1.p',unknown),
    [] ).

cnf(560,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
    file('SWV911-1.p',unknown),
    [] ).

cnf(561,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
    file('SWV911-1.p',unknown),
    [] ).

cnf(562,axiom,
    ( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
    | hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) ),
    file('SWV911-1.p',unknown),
    [] ).

cnf(563,axiom,
    ( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(u,v)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,v,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('SWV911-1.p',unknown),
    [] ).

cnf(564,axiom,
    ( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(u,v)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,v,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('SWV911-1.p',unknown),
    [] ).

cnf(565,axiom,
    ( ~ hBOOL(hAPP(hAPP(u,v),v_xa))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,w,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(w,v),v_xb(u,w))) ),
    file('SWV911-1.p',unknown),
    [] ).

cnf(566,plain,
    equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_COMBK(c_False,tc_bool,u)),
    inference(rew,[status(thm),theory(equality)],[203,373]),
    [iquote('0:Rew:203.0,373.0')] ).

cnf(606,plain,
    equal(hAPP(hAPP(c_Set_Oinsert(u),v),c_COMBK(c_False,tc_bool,u)),hAPP(c_fequal(u),v)),
    inference(rew,[status(thm),theory(equality)],[566,461,203]),
    [iquote('0:Rew:566.0,461.0,203.0,461.0')] ).

cnf(632,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),t_a),
    inference(rew,[status(thm),theory(equality)],[606,561,566]),
    [iquote('0:Rew:606.0,561.0,566.0,561.0')] ).

cnf(633,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a),
    inference(rew,[status(thm),theory(equality)],[606,560,566]),
    [iquote('0:Rew:606.0,560.0,566.0,560.0')] ).

cnf(686,plain,
    ( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(u,v)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,v,t_a)),t_a) ),
    inference(rew,[status(thm),theory(equality)],[606,563,566]),
    [iquote('0:Rew:606.0,563.1,566.0,563.1')] ).

cnf(687,plain,
    ( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(u,v)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,v,t_a)),t_a) ),
    inference(rew,[status(thm),theory(equality)],[606,564,566]),
    [iquote('0:Rew:606.0,564.1,566.0,564.1')] ).

cnf(702,plain,
    ( ~ hBOOL(hAPP(hAPP(u,v),v_xa))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,w,t_a)),t_a)
    | hBOOL(hAPP(hAPP(w,v),v_xb(u,w))) ),
    inference(rew,[status(thm),theory(equality)],[606,565,566]),
    [iquote('0:Rew:606.0,565.1,566.0,565.1')] ).

cnf(758,plain,
    ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))),
    inference(res,[status(thm),theory(equality)],[632,687]),
    [iquote('0:Res:632.0,687.1')] ).

cnf(760,plain,
    ( ~ hBOOL(hAPP(hAPP(v_P_H,u),v_xa))
    | hBOOL(hAPP(hAPP(v_Q_H,u),v_xb(v_P_H,v_Q_H))) ),
    inference(res,[status(thm),theory(equality)],[632,702]),
    [iquote('0:Res:632.0,702.1')] ).

cnf(782,plain,
    ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))),
    inference(res,[status(thm),theory(equality)],[633,686]),
    [iquote('0:Res:633.0,686.1')] ).

cnf(783,plain,
    ( ~ hBOOL(hAPP(hAPP(v_P,u),v_xa))
    | hBOOL(hAPP(hAPP(v_Q,u),v_xb(v_P,v_Q))) ),
    inference(res,[status(thm),theory(equality)],[633,702]),
    [iquote('0:Res:633.0,702.1')] ).

cnf(1374,plain,
    ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
    inference(res,[status(thm),theory(equality)],[783,782]),
    [iquote('0:Res:783.1,782.0')] ).

cnf(1375,plain,
    hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)),
    inference(mrr,[status(thm)],[562,1374]),
    [iquote('0:MRR:562.0,1374.0')] ).

cnf(1376,plain,
    ~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)),
    inference(res,[status(thm),theory(equality)],[760,758]),
    [iquote('0:Res:760.1,758.0')] ).

cnf(1377,plain,
    $false,
    inference(mrr,[status(thm)],[1376,1375]),
    [iquote('0:MRR:1376.0,1375.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWV911-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n016.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jun 14 22:43:31 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.50/0.69  
% 0.50/0.69  SPASS V 3.9 
% 0.50/0.69  SPASS beiseite: Proof found.
% 0.50/0.69  % SZS status Theorem
% 0.50/0.69  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.50/0.69  SPASS derived 579 clauses, backtracked 0 clauses, performed 0 splits and kept 644 clauses.
% 0.50/0.69  SPASS allocated 77750 KBytes.
% 0.50/0.69  SPASS spent	0:00:00.33 on the problem.
% 0.50/0.69  		0:00:00.05 for the input.
% 0.50/0.69  		0:00:00.00 for the FLOTTER CNF translation.
% 0.50/0.69  		0:00:00.01 for inferences.
% 0.50/0.69  		0:00:00.00 for the backtracking.
% 0.50/0.69  		0:00:00.17 for the reduction.
% 0.50/0.69  
% 0.50/0.69  
% 0.50/0.69  Here is a proof with depth 2, length 24 :
% 0.50/0.69  % SZS output start Refutation
% See solution above
% 0.50/0.69  Formulae used in the proof : cls_Collect__def_0 cls_empty__def_0 cls_singleton__conv2_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.50/0.69  
%------------------------------------------------------------------------------